Abstract

This paper introduces empirical likelihood methods for interval estimation and hypothesis testing on volatility measures in some high frequency data environments. We propose a modified empirical likelihood statistic that is asymptotically pivotal under infill asymptotics, where the number of high frequency observations in a fixed time interval increases to infinity. The proposed statistic is extended to be robust to the presence of jumps and microstructure noise. We also provide an empirical likelihood-based test to detect the presence of jumps. Furthermore, we study higher-order properties of a general family of nonparametric likelihood statistics and show that a particular statistic admits a Bartlett correction: a higher-order refinement to achieve better coverage or size properties. Simulation and a real data example illustrate the usefulness of our approach.

摘要

本文介绍了经验似然方法，用于在某些高频数据环境中进行波动率测度的区间估计和假设检验。我们提出了一种改进的经验似然统计量，该统计量在填充渐近性下是渐近关键的，其中固定时间间隔内的高频观测次数增加到无穷大。所提出的统计数据被扩展为对于跳跃和微观结构噪声的存在具有鲁棒性。我们还提供了基于经验的似然性测试来检测跳跃的存在。此外，我们研究了非参数似然统计量的一般族的高阶性质，并表明特定统计量接受Bartlett校正：为了获得更好的覆盖率或大小性质而进行的高阶细化。